Question

How do I find the negative power of a complex number?

Answer 1

Given a complex number of form `a + bi`,it can be proved that any power of it will be of the form `c + di`.
For example, `(a+bi)^2 = (a^2-b^2) + 2abi`

Knowing that, its less scary to try and find bigger powers, such as a cubic or fourth.
Whatsoever, any negative power of a complex number will look like this:
`(a+bi)^-n = 1/(a+bi)^n = 1/(c+di)`
This final form is not acceptable, as it has a division by `i`, but we can use a factoring method to make it better.
`(m+n)(m-n) = m^2-n^2` `->` `(m+ni)*(m-ni) = m^2+n^2`

`1/(c+di)*((c-di))/((c-di)) = (c-di)/(c^2+d^2)`//